This project is part of a long-term effort to improve the quality of the images obtained by positron emission tomography (PET), which has become an important technique for tomographic imaging in diagnostic radiology and nuclear medicine. The project involves computer methods for generating images from the basic detector data of PET scanners, including processing operations to compensate for non-ideal characteristics of the data, and algorithms for image reconstruction from the projection data produced by the initial processing. With the present PET scanners and methods for processing the data, it is found that the images obtained for large patients are of much lower quality than the images for normal-sized patients, because the data set from a PET scan of a large patient contains a larger proportion of scattered photons and a smaller proportion of unscattered photons, compared to the data from a normal-sized patient. The aim of this project is to improve the images obtained in PET through the use of new methods of processing the data that exploit the marked difference between the energy distributions of unscattered and scattered photons. The new energy-based methods will take advantage of the better energy resolution of modern scanners and will enable full use of the excellent energy resolution and timing of the next generation of scintillation crystals and detectors. The methods proposed are general and can be applied to the current conventional PET scanners in a simpler manner than the presently used image based scatter estimation methods. They will also be designed for the needs of the new generation of scanners for time-of-flight PET (TOF-PET), for which adequate scatter correction techniques have not yet been developed. The approach is to develop, implement, test, and evaluate for feasibility, new energy-based methods for PET and TOF-PET involving combined image reconstruction and scatter estimation. These methods will be compared with extensions of the most widely used conventional method, which is the single-scatter- simulation method. The comparison studies will be done using simulated data and using experimental PET data from physical test phantoms. New energy-based methods have the potential to significantly improve the accuracy of the voxel-by-voxel estimates of radiotracer uptake in PET images, which would lead to improvements in the clinical applications of PET, such as PET imaging of cancer, which would in turn have a significant impact on public health. [unreadable] [unreadable] [unreadable]